Method of controlling a wave energy conversion system maximizing the power output

ABSTRACT

The invention is an improved wave energy conversion system ( 1, 2 ) including a model predictive control method for an energy conversion machine ( 1 ) that maximizes the power output by accounting for the energy conversion efficiency and a wave motion prediction ( 3 ).

CROSS REFERENCE TO RELATED APPLICATIONS

Reference is made to International Application No. PCT/2015/055842 filedMar. 19, 2015, and French Application No. 14/52.885 filed Apr. 1, 2014,which applications are incorporated herein by reference in theirentirety.

BACKGROUND OF THE INVENTION

Field of the Invention

The invention relates to the field of devices for converting wave energyto electrical or hydraulic energy.

Description of the Prior Art

Renewable energy resources have generated strong interest for someyears. They are clean, free and inexhaustible, which are major assets ina world facing the inexorable depletion of the available fossilresources and recognizing the need to preserve the planet. Among theseresources, wave energy, a source relatively unknown amidst those widelypublicized, such as wind or solar energy, contributes to the vitaldiversification of the exploitation of renewable energy sources. Thedevices, commonly referred to as “wave energy conversion devices”, areparticularly interesting because they allow electricity to be producedfrom this renewable energy source (the potential and kinetic waveenergy) without greenhouse gas emissions. They are particularly wellsuited for providing electricity to isolated island sites.

BACKGROUND OF THE INVENTION

For example, patent applications FR-2,876,751, FR-2,973,448 andWO-2009/081,042 describe devices which capture the energy produced bythe sea water forces. These devices are made up of a floating supportstructure on which a pendulum is movably mounted with respect to thefloating support. The relative motion of the pendulum with respect tothe floating support is used to produce electrical energy by an energyconverter machine (an electric machine for example). The convertermachine operates as a generator and as a motor. Indeed, in order toprovide a torque or a force driving the mobile energy source, power issupplied to the converter machine to bring it into resonance with thewaves (motor mode). On the other hand, to produce a torque or a forcethat withstands the motion of the mobile source, power is recovered viathe converter machine (generator mode).

The motion of the mobile source is thus controlled by the energyconverter machine to promote energy recovery. In order to optimize theelectrical energy recovered by wave energy conversion systems, variousconverter machine control methods have been considered. Some are notoptimal because the wave motion prediction is not taken intoconsideration. Furthermore, these methods do not account for the energylosses which occur during energy conversion in the wave energyconversion system. For example, patent application FR-2,973,448(WO-2012/131,186) describes such a method.

Other methods combine model predictive control with a wave motionprediction algorithm. However, these algorithms do not allow the energylosses consequent from energy conversion with the wave energy conversionsystem to be taken into account. This does not enable to an optimumcontrol maximizing the recovered energy. For example, the followingdocument describes such a method: Giorgio Bacelli, John Ringwood andJean-Christophe Gilloteaux, “A control system for a Self-Reacting PointAbsorber Wave Energy Converter Subject to Constraints”, in: Proceedingsof 18th IFAC World Congress, International Federation of AutomaticControl (IFAC), 2011, pp. 11387-11392.

SUMMARY OF THE INVENTION

The invention improves the operation of a wave energy conversion systemby use of a predictive control method using model which provides anenergy conversion machine that maximizes the power output by accountingfor energy conversion efficiency and wave motion prediction.

The invention is a method for controlling a wave energy conversionsystem that converts the energy of waves to electrical or hydraulicenergy, the wave energy conversion system comprising at least one mobilesystem that cooperates with at least one energy conversion machine, andthe mobile system has an oscillating motion with respect to the energyconversion machine. For this method, the following stages are carriedout:

a) constructing a dynamic model of the wave energy conversion systemrelating the velocity of the mobile system to the force exerted by thewaves on the mobile system and to the force exerted by the energyconversion machine on the mobile system,

b) constructing an energy model of the wave energy conversion systemrelating an average power generated by the energy conversion machine tothe force exerted by the energy conversion machine on the mobile system,to the velocity of the mobile system and to an efficiency of the waveenergy conversion machine system;

c) predicting a force exerted by the waves on the mobile system for apredetermined time period;

d) determining a control value of the force exerted by the wave energyconversion machine on the mobile system maximizing the average powergenerated by the wave energy conversion machine, by use of theprediction of a force exerted by the waves on the mobile system, of thedynamic model and of said the other wave energy model; and

e) controlling the converter machine by system of a control value.

According to a variant embodiment of the invention, the force exerted bythe waves on the mobile system is predicted by at least one measurementor one estimation of the force exerted by the waves on the mobilesystem, using a set of pressure detectors arranged in a vicinity of themobile system or force sensors arranged between the mobile system andthe wave energy conversion machine.

Alternatively, the force exerted by the waves on the mobile system ispredicted by measuring waves upstream from the wave energy conversionsystem.

Advantageously, the dynamic model of the wave energy conversion systemis constructed by a model of dynamics of the energy conversion machineand of a model of a mechanical and hydrodynamic part of the energyconversion system.

Preferably, a model of the dynamics of the wave energy conversionmachine is written using equations of the form: x_(a)=A_(a)^(c)x_(a)+B_(a) ^(c)u_(c) and u=C_(a) ^(c)x_(a), and the model ofmechanical and hydrodynamic part is written using equations of the form:x_(s)=A_(s) ^(c)x_(s)+B_(s) ^(c)(w−u) and v=C_(s) ^(c)x_(s), with x_(a)being the state vector of the converter machine, x_(s) being the statevector of a mechanical and a hydrodynamic part, A_(a) ^(c), B_(a) ^(c),C_(a) ^(c), A_(s) ^(c), B_(s) ^(c) and C_(s) ^(c) being dynamicmatrices, inputs, being outputs of a dynamic model of the wave energyconversion machine and of a mechanical and hydrodynamic part, u_(c)being the control of the force exerted by energy conversion machine onthe mobile system, w being the control of the force exerted by the waveson the mobile system, u being the force exerted by said the energyconversion machine on the mobile system and v being the velocity ofmobile system in relation to the wave energy conversion machine.

Advantageously, a Kalman filter is notably synthesized from the twolinear models by using a state observer modeling the state of thesystem.

According to an aspect of the invention, the wave energy conversionmodel is written with a formula of the type:

${P_{m}^{c} = {{- \frac{1}{T}}{\int_{t = 0}^{T}{\eta \; {uvdt}}}}},$

with P_(m) ^(c) being an average power output, t time, T being apredetermined duration, η being an energy conversion efficiency, u beinga force exerted by the converter machine on the mobile system and vbeing velocity of the mobile system in relation to said the wave energyconverter machine.

Advantageously, the efficiency η is a function of force u exerted by theconverter machine on the mobile system and of velocity v of the mobilesystem in relation to said the wave energy conversion machine.

According to a variant embodiment, the efficiency η is calculated with aformula of the type:

${\eta ({uv})} = \left\{ \begin{matrix}\eta_{0} & {{{if}\mspace{14mu} {uv}} \geq 0} \\\frac{1}{\eta_{0}} & {{{if}\mspace{14mu} {uv}} < 0}\end{matrix} \right.$

with η₀ being motor and generator efficiency of the wave energyconversion machine, with 0≦η₀≦1.

Alternatively, the efficiency η is calculated with a formula of thetype:

${\eta ({uv})} = {{{- \frac{\frac{1}{\eta_{0}} - \eta_{0}}{\pi}}{\arctan \left( \frac{\pi \; r_{a}{uv}}{2} \right)}} + \frac{\frac{1}{\eta_{0}} - \eta_{0}}{2} + \eta_{0}}$

with η₀ being motor and generator efficiency of the wave energyconversion machine, with 0≦η₀≦1, and r_(a) being a smoothing parameterof the function.

According to the invention, maximizing average power output is achievedby an optimization algorithm constrained by minimum and maximum valuesof force exerted by the energy conversion machine on the mobile systemand constraints on a state of the system.

Preferably, maximization of an average power output is an optimizationalgorithm of interior point type.

According to an embodiment of the invention, c), d) and e) are repeatedfor a model of predictive control with moving horizon.

Advantageously, the wave energy conversion machine is an electric orhydraulic machine.

BRIEF DESCRIPTION OF THE DRAWINGS

Other features and advantages of the method according to the inventionwill be clear from reading the description hereafter, with reference tothe accompanying figures wherein:

FIG. 1 illustrates stages of the method according to the invention;

FIG. 2 illustrates two curves for two examples of equations ofefficiency as a function of an instantaneous mechanical power (productuv);

FIG. 3 illustrates curves of an instantaneous mechanical power (productuv) as a function of time for various efficiency values;

FIG. 4 illustrates a model of predictive control with a moving horizonaccording to the invention;

FIG. 5 illustrates an example of a wave energy conversion system;

FIG. 6 illustrates an amplitude as a function of frequency of variouswave motion types which are simulated;

FIG. 7 shows curves relative to displacement, velocity, control andinstantaneous mechanical power (product uv) for the wave energyconversion system of FIG. 5 and a wave motion of HO 1 type of FIG. 6according to a method of the prior art and according to the controlmethod of the invention; and

FIG. 8 corresponds to FIG. 7 for a wave motion of HO 5 type in FIG. 6.

DETAILED DESCRIPTION OF THE INVENTION

The invention is a method of controlling a wave energy conversion systemthat comprises at least one mobile system cooperating with at least onewave energy conversion machine also referred to as Power Take-Off (PTO).The mobile system has an oscillating motion with respect to the waveenergy conversion machine, under the action of the waves (or wavemotion) and of the wave energy conversion machine. The wave energyconversion machine converts mechanical energy of motion of the mobilesystem into electrical energy. The wave energy conversion machine cantherefore be an electric or a hydraulic machine.

Notations

The following notations are used in the description below:

-   -   u is force exerted by the converter machine on the mobile means,        and        -   u_(c) is control value of force exerted by the wave energy            conversion machine on the mobile system,    -   w is force exerted by waves on the mobile system,    -   v is velocity of the mobile system in relation to the converter        machine,    -   x_(a) is a state vector of the wave energy conversion machine of        the wave energy conversion system,    -   x_(s) is a state vector of a mechanical and a hydrodynamic part        of the wave energy conversion system;    -   A_(a) ^(c), B_(a) ^(c), C_(a) ^(c), A_(s) ^(c), B_(s) ^(c) and        C_(s) ^(c) are dynamic matrices, inputs, outputs of dynamic        models of the wave energy conversion machine and of the        mechanical and the hydrodynamic part. The model can be        calculated by a balance of forces or an experimental        identification procedure. If the model is linear, it can be        represented by matrices (it is a formalism), with:    -   P_(m) ^(c) being average power output;    -   t being time;    -   T_(f) being a predetermined duration;    -   η being an energy conversion efficiency; with        -   η₀ being motor and generator efficiency of the wave energy            conversion machine; these are manufacturer's data or            experimentally determined data; and    -   r_(a) is a predetermined smoothing parameter of an efficiency        function.

In the description below and in the claims, the terms waves, sea wavesand wave motion are considered to be equivalent.

The invention relates to a method of controlling a wave energyconversion system. FIG. 1 shows the various stages of the methodaccording to the invention:

1. Construction of a dynamic model (MOD DYN)

2. Construction of an energy model (MOD ENE)

3. Prediction of the force exerted by the waves (PRED)

4. Estimation of the state of the system (ETAT)

5. Determination of the control value (VAL)

6. Control of the converter machine (COM).

Stages 1 and 2 are stages that can be carried out beforehand and arepart of a calibration procedure when the machine is installed. Stages 3to 6 are carried out in real time, in a real-time loop (BTR).

Stage 1—Construction of a Dynamic Model (MOD DYN)

In this stage, a dynamic model of the wave energy conversion system isconstructed. The dynamic model represents the dynamic behaviorreflecting the motion of the elements making up the wave energyconversion system under action of waves and under action of the waveenergy conversion machine. The dynamic model is a model that relatesvelocity of the mobile system to a force exerted by the on the mobilesystem and to force exerted by the wave energy conversion machine on themobile system.

According to an embodiment of the invention, the dynamic model cancomprise a linear model of dynamics of the wave energy conversionmachine. This linear model can be written in form as follows:x_(a)=A_(a) ^(c)x_(a)+B_(a) ^(c)u_(c) and u=C_(a) ^(c)x_(a). The dynamicmodel can also comprise a linear model of a mechanical and ahydrodynamic part of the wave energy conversion system. This linearmodel can be written in the form as follows: x_(s)=A_(s) ^(c)x_(s)+B_(s)^(c)(w−u) and v=C_(s) ^(c)x_(s).

Stage 2—Construction of an Energy Model (MOD ENE)

In this stage, an energy model of the wave energy conversion system isconstructed. The energy model represents an energy balance between theenergy generated by the wave energy conversion machine (that is theenergy supplied to the grid) and the wave energy. According to theinvention, this model accounts for an imperfect efficiency of conversionof, mechanical energy into electrical or hydraulic energy, and of theimperfect efficiency of conversion of electrical or hydraulic energyinto mechanical energy. The energy model relates the average powergenerated by the wave energy conversion machine to a force exerted bythe wave energy conversion machine on the mobile system, to velocity ofthe mobile system and to efficiency of energy converters.

According to an embodiment of the invention, the energy model of thewave energy conversion system can be determined from the average powerthat is extracted for a duration T, which can be calculated with aformula of the type:

$P_{m}^{\; c} = {{- \frac{1}{T}}{\int_{t = 0}^{T}{\eta \; {{uvdt}.}}}}$

The definition of the above average power output is such that theaverage power has a negative sign if the energy is extracted from thesystem and for example supplied to the power grid. A maximization of theaverage power output therefore corresponds to a minimization of thispower.

According to the invention, function η is used to model an imperfectefficiency of the energy conversion chain. In this case, the amount ofenergy generated in motor mode is decreased and a cost of energysupplied to the system (to bring it into resonance with the waves inmotor mode) increases. A simple model using the hypothesis thatefficiency η₀ is the same in motor and generator mode can be writtenwith a first equation (Eq 1):

${\eta ({uv})} = \left\{ {\begin{matrix}\eta_{0} & {{{if}\mspace{14mu} {uv}} \geq 0} \\\frac{1}{\eta_{0}} & {{{if}\mspace{14mu} {uv}} < 0}\end{matrix}.} \right.$

Another possibility for modelling efficiency η avoiding the use of adiscontinuity can be written with a second equation (Eq 2):

${\eta ({uv})} = {{{- \frac{\frac{1}{\eta_{0}} - \eta_{0}}{\pi}}{\arctan \left( \frac{\pi \; r_{a}{uv}}{2} \right)}} + \frac{\frac{1}{\eta_{0}} - \eta_{0}}{2} + {\eta_{0}.}}$

The two options (Eq 1 and Eq 2) are illustrated in FIG. 2 as a functionof product uv. The discontinuity of the first equation (Eq 1), unlikethe second equation (Eq 2), can be observed in this figure. Function ηcan also model other energy losses.

Stage 3—Prediction of the Force Exerted by the Waves (PRED)

In this stage, force exerted by the waves on the mobile system ispredicted in real time for a future period of predetermined durationT_(f). This predetermined duration T_(f) can be short, ranging forexample from 5 to 10 seconds. A prediction method is then selected andapplied to the time being considered.

According to an embodiment of the invention, one option is estimating ormeasuring in real time force exerted on the mobile system by the wavemotion, with for example a set of pressure detectors arranged in avicinity of the mobile system or force sensors arranged between themobile system and the wave energy conversion machine, or wave elevationsensors. For the prediction, the force exerted on the mobile means bythe wave motion can be extrapolated using, for example, anautoregressive model identified online.

According to an alternative, the force exerted by waves on the mobilesystem is predicted using a set of detectors arranged upstream from thedevice. These detectors can notably measure the amplitude and thefrequency of the waves.

Stage 4—Estimation of the State of the System (ETAT)

The current state of the wave energy conversion system is determined inreal time. For this stage, the current state can be estimated by use ofa system state observer. This state observer can be achieved bysynthesis of a Kalman filter from a dynamic model of the wave energyconversion system. For example, the observer is constructed from thelinear models described in stage 1.

Furthermore, the observer can take current control of the convertermachine into account to determine a current state of the wave energyconversion system, for example by use of control at times preceding thetime being considered.

Stage 5—Determination of the Control Value (VAL)

In this stage, a control value of the force exerted by the wave energyconversion machine on the mobile system is determined in real time. Thecontrol value maximizes the average power generated by the convertermachine. Determination is therefore performed using prediction of forceexerted by the waves (Stage 3), the dynamic model (Stage 1) and anenergy model (Stage 2). Furthermore, this determination can be achievedby taking a state of the system into account (Stage 4).

Using prediction of the force exerted by the waves gives the predictivecharacteristic of the control method according to the invention. Usingan energy model accounting for energy conversion efficiency involvesconsideration energy losses, which enables an optimum control thatmaximizes the average power generated by the wave energy conversionmachine.

Indeed, if efficiency η is different from 1, the product between controlu and optimum velocity v changes significantly due to cost of the energysupplied to the machine, notably related to the energy losses, as shownin FIG. 3. In this figure, the curves show, for one example, product uvas a function of time for different values of efficiency η₀, which iswhy it is important to take efficiency into account in the calculationof the control.

With the formulations of the dynamic and energy models, the search forthe optimum control with constraints on control u and on the state ofthe system x can be formulated in a general manner: min_(u) _(c) P_(m)^(c) as a function of the models and the following constraints:u_(min)<u<u_(max) and x_(min)<x<x_(max). For minimization of the averagepower output, variable u_(c) can be parameterized. One option is toselect a variable u_(c) that is piecewise constant.

According to an embodiment of the invention, maximization of the averagepower output P_(m) ^(c) is performed by means of an optimizationalgorithm.

According to a variant embodiment of the invention, in order to smooththe control and to avoid unwanted oscillations, a penalty for thevariations of u_(c) can be added to the target function.

According to an embodiment of the invention, a model predictive control(MPC) with a moving horizon is applied for real-time calculation of acontrol:

1. At a current step, step i which is the state of the system isestimated (stage 4) and the wave force is predicted (stage 3). Theoptimum control on a horizon limited to the predetermined period T(around 5 sec) is calculated from these values. This gives a series ofoptimum controls u_(c,i) of length n.

2. The first element of the series of optimum controls u_(c,i) isapplied to the system as the target value for the converter machine(PTO). The value is maintained constant during a time step.

3. At a next step, step i+1, a state of the system is estimated (stage4) and the wave force is predicted (stage 3). The optimum control on ahorizon limited to the predetermined period T is calculated from thesevalues. The initial values for this optimization are selected fromresults of a previous step (from the second input of u_(c,i) to the lastvalue that is repeated once). Optimization provides a new series ofoptimum controls u_(c,i+1) of length n.

4. The first element of the new series of optimum controls u_(c,i+1) isapplied.

These stages 1 to 4 are repeated for each time step.

This model predictive control (MPC) with moving horizon is illustratedin FIG. 4. This figure shows the velocity v and control u_(c) curves fortwo consecutive time steps: i and i+1. PA indicates the past of theconsidered time, AV is the future of the considered time, PRED iindicates the velocity prediction at time i and PRED i+1 is the velocityprediction at time i+1. It can be noted in this figure that theprediction has been modified between the two time steps, even though thegeneral form is similar. It can also be observed that the control hasbeen slightly modified between the two time steps.

The algorithms that solve optimization problems are iterativealgorithms. Since the time allowed for executing them is limited in realtime, it is important for all the steps to give solutions that satisfythe constraints, in cases where it would be necessary to end thealgorithm before convergence. An algorithm providing upon each iterationvalues that satisfy the constraints, such as for example an algorithm ofinterior point type, can be used to solve the optimization problem thatgives the optimum control.

Stage 6—Control of the Converter Machine (COM)

In this stage, the converter machine is controlled as a function ofvalue determined in the previous stage. The wave conversion energymachine (electric or hydraulic machine) is therefore actuated toreproduce a new value of force u_(c) as determined in stage 5.

For example, a new expression of force u_(c) exerted by the wave energyconversion machine on the mobile system is applied to the electricmachine. Controlling the electric machine so that it applies force u_(c)to the mobile means is achieved by modifying the electric currentapplied to the electric machine. More precisely, to provide a torque ora force that drives the mobile system, a current is applied by supplyingan electric power.

On the other hand, to produce a torque or a force withstanding themotion of the mobile means, a current is applied by recovering electricpower.

Application Example

A non limitative example of a wave energy conversion system is anoscillating buoy as shown in FIG. 5. This wave energy conversion systemcomprises a buoy 2 as the mobile means of mass m, a converter machine 1of damping d and elasticity k that is stationary. The buoy is subjectedto an oscillating motion through waves 3 and to hydraulic forces(ordinary differential equation ODE of order 5).

In this example, a model predictive control MPC is compared with amoving horizon according to the invention with a PI (ProportionalIntegral) control according to the prior art. Five different sea statesare considered, whose (smoothed) spectra are shown in FIG. 6. Thisfigure shows the curves, for five sea states (wave motions HO 1, HO 2,HO 3, HO 4 and HO 5), of the wave elevation h in meters as a function offrequency fin Hertz.

For the control according to the invention, the dynamic model takes intoaccount the dynamics of the mechanical and hydrodynamic part with afifth-order linear system and the actuator dynamics with a second-orderlinear system. The wave energy conversion machine stress is limited andthe non-linear efficiency, corresponding to

${\eta ({uv})} = \left\{ {\begin{matrix}\eta_{0} & {{{if}\mspace{14mu} {uv}} \geq 0} \\\frac{1}{\eta_{0}} & {{{if}\mspace{14mu} {uv}} < 0}\end{matrix},} \right.$

with η₀=0.7, is modelled and a saturation of the control can beachieved.

A conventional control according to the prior art for a wave energyconversion system loops the PTO control on the velocity of the mobilemeans via a PI control:

u _(c) =−k _(p)∫_(t) ₀ ^(t) vdτ−k _(v) v.

For the comparison with the model predictive control according to theinvention, gains ^(k)p and ^(k)v are optimally calibrated for all thesea states considered.

The results of the comparison between the MPC strategy according to theinvention (INV) and the PI strategy according to the prior art (AA) aresummed up in Table 1. The energy generation gain ranges between 16% and50%.

TABLE 1 Average power of the model predictive control and of aconventional PI control Max. pos. Max. vel. P_(m) PI P_(m) MPC Gainratio ratio (AA)/kW (INV)/kW P_(m) (MPC/PI) (MPC/PI) Wave −2.83 −4.2650.43% 1.31 1.48 motion 1 Wave −8.64 −11.89 37.54% 0.89 0.88 motion 2Wave −16.42 −20.76 26.44% 0.81 0.91 motion 3 Wave −24.44 −29.26 19.75%0.88 0.91 motion 4 Wave −32.14 −37.14 15.55% 0.90 0.97 motion 5

The trajectory of the system d is in rad, velocity v is in rad/s,control u is in 10⁶ Nm and product uv is in kW, controlled by MPC (INV)and PI (AA), as shown in FIGS. 7 and 8 respectively for a wave motion HO1 and HO 5 (see FIG. 6). It can be seen that the maximum position andthe maximum velocity are reduced (except in the case of wave motion HO1, which is very weak and does not excite high oscillations).

1-14. (canceled)
 15. A method of controlling a wave energy conversionsystem that converts energy of waves into electrical or hydraulicenergy, the wave energy conversion system comprising at least one mobilesystem that cooperates with at least one wave energy conversion machine,and the mobile system having an oscillating motion with respect to theat least one wave energy conversion machine, comprising: a) constructinga dynamic model of the wave energy conversion system relating velocityof the at least one mobile system to a force exerted by the waves on theat least one mobile system and to force exerted by the at least one waveenergy conversion machine on the mobile system; b) constructing anenergy model of the wave energy conversion system relating an averagepower generated by the at least one wave energy conversion machine tothe force exerted by the at least one wave energy conversion machine onthe at least one mobile system, to a velocity of the mobile system andto efficiency of the at least one wave energy conversion system; c)predicting the force exerted by waves (3) on the mobile system for apredetermined time period; d) determining a control value of the forceexerted by the at least one wave energy conversion machine on the atleast one mobile system which maximizes average power generated by theat least one wave energy conversion machine, by use of the predictedforce exerted by the waves on the at least one mobile system, of thedynamic model and of the energy model; and e) controlling the at leastone wave energy conversion machine with the control value.
 16. A methodas claimed in claim 15, wherein the force exerted by the waves on the atleast one mobile system is predicted by at least one of a measurementand an estimation of the force exerted by the waves on the at least onemobile system, using a set of pressure detectors in a vicinity of the atleast one mobile system or force sensors between the at least one mobilesystem and the at least one wave energy conversion machine.
 17. A methodas claimed in claim 15, wherein the force exerted by the waves on the atleast one mobile system is predicted by measurement of the wavesupstream from the at least one wave energy conversion system.
 18. Amethod as claimed in claim 15, wherein the dynamic model of the at leastone wave energy conversion system is constructed using a model ofdynamics of the at least one wave energy conversion machine and of amodel of a mechanical and a hydrodynamic part of the wave energyconversion system.
 19. A method as claimed in claim 16, wherein thedynamic model of the at least one wave energy conversion system isconstructed using a model of dynamics of the at least one wave energyconversion machine and of a model of a mechanical and a hydrodynamicpart of the wave energy conversion system.
 20. A method as claimed inclaim 17, wherein the dynamic model of the at least one wave energyconversion system is constructed using a model of dynamics of the atleast one wave energy conversion machine and of a model of a mechanicaland a hydrodynamic part of the wave energy conversion system.
 21. Amethod as claimed in claim 18, wherein the model of dynamics of the atleast one wave energy conversion machine is written with equations:x_(a)=A_(a) ^(c)x_(a)+B_(a) ^(c)u_(c) and u=C_(a) ^(c)x_(a), and themodel of the mechanical and hydrodynamic part is written usingequations: x_(s)=A_(s) ^(c)x_(s)+B_(s) ^(c)(w−u) and v=C_(s) ^(c)x_(s),with x_(a) being a state vector of the wave energy conversion machine,x_(s) being a the state vector of the mechanical and hydrodynamic part,A_(a) ^(c), B_(a) ^(c), C_(a) ^(c), A_(s) ^(c), B_(s) ^(c) and C_(s)^(c) being the dynamic matrices, inputs, outputs of the dynamic modelsof the at least one wave energy conversion machine and of mechanical andhydrodynamic part, u_(c) being the control of the force exerted by the aleast one wave energy conversion machine on the at least one mobilesystem, w being control of the force exerted by the waves on the atleast one mobile system, u being exerted by the at least one wave energyconversion machine on the at least one mobile system and v beingvelocity of the at least one mobile system in relation to the at leastone wave energy conversion machine.
 22. A method as claimed in claim 17,wherein the model of dynamics of the at least one wave energy conversionmachine is written with equations: x_(a)=A_(a) ^(c)x_(a)+B_(a) ^(c)u_(c)and u=C_(a) ^(c)x_(a), and the model of the mechanical and hydrodynamicpart is written using equations: x_(s)=A_(s) ^(c)x_(s)+B_(s) ^(c)(w−u)and v=C_(s) ^(c)x_(s), with x_(a) being a state vector of the waveenergy conversion machine, x_(s) being a the state vector of themechanical and hydrodynamic part, A_(a) ^(c), B_(a) ^(c), C_(a) ^(c),A_(s) ^(c), B_(s) ^(c) and C_(s) ^(c) being the dynamic matrices,inputs, outputs of the dynamic models of the at least one wave energyconversion machine and of mechanical and hydrodynamic part, u_(c) beingthe control of the force exerted by the a least one wave energyconversion machine on the at least one mobile system, w being control ofthe force exerted by the waves on the at least one mobile system, ubeing exerted by the at least one wave energy conversion machine on theat least one mobile system and v being velocity of the at least onemobile system in relation to the at least one wave energy conversionmachine.
 23. A method as claimed in claim 16, wherein the model ofdynamics of the at least one wave energy conversion machine is writtenwith equations: x_(a)=A_(a) ^(c)x_(a)+B_(a) ^(c)u_(c) and u=C_(a)^(c)x_(a), and the model of the mechanical and hydrodynamic part iswritten using equations: x_(s)=A_(s) ^(c)x_(s)+B_(s) ^(c)(w−u) andv=C_(s) ^(c)x_(s), with x_(a) being a state vector of the wave energyconversion machine, x_(s) being a the state vector of the mechanical andhydrodynamic part, A_(a) ^(c), B_(a) ^(c), C_(a) ^(c), A_(s) ^(c), B_(s)^(c) and C_(s) ^(c) being the dynamic matrices, inputs, outputs of thedynamic models of the at least one wave energy conversion machine and ofmechanical and hydrodynamic part, u_(c) being the control of the forceexerted by the a least one wave energy conversion machine on the atleast one mobile system, w being control of the force exerted by thewaves on the at least one mobile system, u being exerted by the at leastone wave energy conversion machine on the at least one mobile system andv being velocity of the at least one mobile system in relation to the atleast one wave energy conversion machine.
 24. A method as claimed inclaim 18, wherein a Kalman filter is synthesized from the two linearmodels by use of a state observer for observing a state of the system.25. A method as claimed in claim 21, wherein a Kalman filter issynthesized from the two linear models by use of a state observer forobserving a state of the system.
 26. A method as claimed in claim 15,wherein the energy model is written with a formula:${P_{m}^{\; c} = {{- \frac{1}{T}}{\int_{t = 0}^{T}{\eta \; {uvdt}}}}},$with P_(m) ^(c) being average power output, t being time, T being apredetermined duration, η being an energy conversion efficiency, u beinga force exerted by the at least one wave energy conversion machine onthe at least one mobile system and v being velocity of the at least onemobile system in relation to the at least one wave energy conversionmachine.
 27. A method as claimed in claim 16, wherein the energy modelis written with a formula:${P_{m}^{\; c} = {{- \frac{1}{T}}{\int_{t = 0}^{T}{\eta \; {uvdt}}}}},$with P_(m) ^(c) being average power output, t being time, T being apredetermined duration, η being an energy conversion efficiency, u beinga force exerted by the at least one wave energy conversion machine onthe at least one mobile system and v being velocity of the at least onemobile system in relation to the at least one wave energy conversionmachine.
 28. A method as claimed in claim 17, wherein the energy modelis written with a formula:${P_{m}^{\; c} = {{- \frac{1}{T}}{\int_{t = 0}^{T}{\eta \; {uvdt}}}}},$with P_(m) ^(c) being average power output, t being time, T being apredetermined duration, η being an energy conversion efficiency, u beinga force exerted by the at least one wave energy conversion machine onthe at least one mobile system and v being velocity of the at least onemobile system in relation to the at least one wave energy conversionmachine.
 29. A method as claimed in claim 18, wherein the energy modelis written with a formula:${P_{m}^{\; c} = {{- \frac{1}{T}}{\int_{t = 0}^{T}{\eta \; {uvdt}}}}},$with P_(m) ^(c) being average power output, t being time, T being apredetermined duration, η being an energy conversion efficiency, u beinga force exerted by the at least one wave energy conversion machine onthe at least one mobile system and v being velocity of the at least onemobile system in relation to the at least one wave energy conversionmachine.
 30. A method as claimed in claim 21, wherein the energy modelis written with a formula:${P_{m}^{\; c} = {{- \frac{1}{T}}{\int_{t = 0}^{T}{\eta \; {uvdt}}}}},$with P_(m) ^(c) being average power output, t being time, T being apredetermined duration, η being an energy conversion efficiency, u beinga force exerted by the at least one wave energy conversion machine onthe at least one mobile system and v being velocity of the at least onemobile system in relation to the at least one wave energy conversionmachine.
 31. A method as claimed in claim 24, wherein the energy modelis written with a formula:${P_{m}^{\; c} = {{- \frac{1}{T}}{\int_{t = 0}^{T}{\eta \; {uvdt}}}}},$with P_(m) ^(c) being average power output, t being time, T being apredetermined duration, η being an energy conversion efficiency, u beinga force exerted by the at least one wave energy conversion machine onthe at least one mobile system and v being velocity of the at least onemobile system in relation to the at least one wave energy conversionmachine.
 32. A method as claimed in claim 26, wherein efficiency η is afunction of force u exerted by the at least one wave energy conversionmachine on the at least one mobile system and of velocity v of the atleast one mobile system in relation to the at least one wave energyconversion machine.
 33. A method as claimed in claim 26, wherein theefficiency η is calculated with a formula:${\eta ({uv})} = \left\{ \begin{matrix}\eta_{0} & {{{if}\mspace{14mu} {uv}} \geq 0} \\\frac{1}{\eta_{0}} & {{{if}\mspace{14mu} {uv}} < 0}\end{matrix} \right.$ with η₀ being motor and generator efficiency ofthe at least one wave energy conversion machine, with 0≦η₀≦1.
 34. Amethod as claimed in claim 26, wherein the efficiency η is calculatedwith a formula: ${\eta ({uv})} = \left\{ \begin{matrix}\eta_{0} & {{{if}\mspace{14mu} {uv}} \geq 0} \\\frac{1}{\eta_{0}} & {{{if}\mspace{14mu} {uv}} < 0}\end{matrix} \right.$ with η₀ being motor and generator efficiency ofthe at least one wave energy conversion machine, with 0≦η₀≦1.
 35. Amethod as claimed in claim 32, wherein efficiency η is calculated with aformula:${\eta ({uv})} = {{{- \frac{\frac{1}{\eta_{0}} - \eta_{0}}{\pi}}{\arctan \left( \frac{\pi \; r_{a}{uv}}{2} \right)}} + \frac{\frac{1}{\eta_{0}} - \eta_{0}}{2} + \eta_{0}}$with η₀ being motor and generator efficiency of the at least one waveenergy conversion machine, with 0≦η₀≦1, and r_(a) being a smoothingparameter of the function.
 36. A method as claimed in claim 33, whereinefficiency η is calculated with a formula:${\eta ({uv})} = {{{- \frac{\frac{1}{\eta_{0}} - \eta_{0}}{\pi}}{\arctan \left( \frac{\pi \; r_{a}{uv}}{2} \right)}} + \frac{\frac{1}{\eta_{0}} - \eta_{0}}{2} + \eta_{0}}$with η₀ being motor and generator efficiency of the at least one waveenergy conversion machine, with 0≦η₀≦1, and r_(a) being a smoothingparameter of the function.
 37. A method as claimed in claim 15, whereinmaximizing average power output is achieved of an optimization algorithmconstrained by minimum and maximum values of a force exerted by the atleast one wave energy conversion machine on the at least one mobilesystem and constraints on a state of the at least one wave energyconversion system.
 38. A method as claimed in claim 37, whereinmaximization of average power output used an optimization algorithm ofan interior point type.
 39. A method as claimed in claim 15, wherein c),d) and e) are repeated for a model predictive control with a movinghorizon.
 40. A method as claimed in claim 15, wherein the at least onewave energy conversion machine is an electric or hydraulic machine.